Hi,
Thanks for your inquiry.
Your PCB design looks fine by mounting BME280 on a tiny PCB that is separated from the main PCB. This way the temperature change on the main PCB will not affect BME280 temperature and humidity measurements.
According to BME280 datasheet the typical temperature accuracy is +/-1C and humidity accuracy of +/-3%RH. I am not sure why 2 minutes later after BME280 is powered on the temperature measurement goes up while the humidity measurement goes down. It should be stable from the beginning. Maybe you can try to place a piece of Kapton tape to cover BME280 vent hole before hotgun soldering and oven reflow. You can remove the tape after soldering. This way can prevent BME280 from contamination.
In addition, you can use your reference meter to do two temperature points temperature and humidity calibration. After you determine the calibration parameters, you can save them in your MCU's flash memory and apply them to future BME280 measurements to get the compensated final values. Then you can compare the BME280 measurements to the reference meter to check the accuracy.
Thanks.
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